Explored are various aspects of drawing graphs on surfaces. The Euler's formula, Kuratowski's theorem and the drawing of graphs in the plane with as few crossings as possible are discussed. Some applications including embedding of graphs and coloring of maps are included. (YP)

This document argues that qualitative graphing is an effective introduction to mathematics as a construction for communication of ideas involving quantitative relationships. It is suggested that with little or no prior knowledge of Cartesian coordinates or analytic descriptions of graphs using equations students can successfully grasp concepts of…

This publication contains reference materials and activities for teachers in a staff development program in New York City, teaching grades 3 and 6. The program combines content and methodology. Sections in the publication include: (1) Student Verbalization Resources; (2) Manipulative Resources; (3) Probability, Statistics, and Graph Resources; (4)…